Integrated Wellbore Caliper

ABSTRACT

Systems and methods are provided for an integrated caliper measurement obtained based on caliper measurements from at least two downhole tools. In one example, a system for obtaining such an integrated caliper includes several caliper tools and data processing circuitry. The caliper tools may respectively obtain caliper measurements of a wellbore. The data processing circuitry may assign respective weights to the respective caliper measurements and combine the weighted caliper measurements to obtain an integrated caliper measurement. The confidence factors may be determined based at least partly on at least two of a plurality of weighting functions. These weighting functions may each relate a confidence of the caliper measurements to an environmental or drilling characteristic occurring when the caliber measurements are obtained.

BACKGROUND

This disclosure relates to an integrated caliper measurement of a wellbore obtained using weighted values of different caliper measurements of the wellbore.

This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present techniques, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions.

Logging-while-drilling (LWD) tools are downhole tools that can obtain logging measurements while a wellbore is being drilled. LWD tool may collect information about the geological formation surrounding the wellbore as well as information relating to the wellbore itself. One such LWD tool is known as an LWD caliper tool, which provides a measurement of the diameter of the wellbore at various depths. Caliper measurements are used in a variety of operations, including drilling, cementing, and evaluation of the geological formation. During drilling, for example, the caliper data can be used to monitor the wellbore condition (e.g., identifying possible wellbore washout and/or impending wellbore instability), thus allowing the driller to take remedial action. During well completion, the caliper data can be used to accurately evaluate the volume of cement to fill the casing annulus, as well as aiding in the selection of casing points. A reliable caliper may also be useful during logging to correct some formation evaluation measurements for wellbore size and to evaluate the quality of almost all other LWD logs. The caliper measurements can also be used to plan services, such as dip meters or formation testers, that may be affected by unfavorable wellbore conditions.

A variety of tools have been developed to obtain LWD caliper measurements, including ultrasonic tools and radiation-based density tools. None of these tools, however, can provide a reliable answer in all drilling environments and conditions. For example, a caliper measurement from the ultrasonic tool has a range that is limited by eccentering, mud weight, and acoustic impedance contrast between drilling mud and the geological formation. Meanwhile, the radiation-based caliper measurements may be available substantially only when the radiation-based tool is rotating. Thus, in the often-valuable sections of the geological formation where the LWD tool is “sliding”—moving through the geological formation without having to rotate—the radiation-based density caliper measurement may not be valid. While calipers from different types of tools may be accurate at different times and under different conditions, any single caliper from one particular tool may not be trustworthy under all wellbore and operating conditions.

SUMMARY

A summary of certain embodiments disclosed herein is set forth below. It should be understood that these aspects are presented merely to provide the reader with a brief summary of these certain embodiments and that these aspects are not intended to limit the scope of this disclosure. Indeed, this disclosure may encompass a variety of aspects that may not be set forth below.

Embodiments of the disclosure relate to systems and methods for an integrated caliper measurement obtained based on caliper measurements from at least two downhole tools or techniques. In one example, a system for obtaining such an integrated caliper includes several caliper tools and data processing circuitry. The caliper tools may respectively obtain caliper measurements of a wellbore. The data processing circuitry may assign respective weights to the respective caliper measurements and combine the weighted caliper measurements to obtain an integrated caliper measurement.

In a second example, one or more tangible non-transitory machine-readable media may store instructions to receive a first caliper measurement deriving from a first downhole tool, a second caliper measurement deriving from a second downhole tool, and one or more conditions under which the first downhole tool obtained the first caliper measurement and under which the second downhole tool obtained the second caliper measurement. The media may also store instructions to determine a first confidence factor—representing a degree of confidence that the first caliper measurement is accurate based at least in part on the one or more conditions—and a second confidence factor—representing a degree of confidence that the second caliper measurement is accurate based at least in part on the one or more condition. The media may also store instructions to determine an integrated caliper measurement using the first caliper measurement, the first confidence factor, the second caliper measurement, and the second confidence factor.

In a third example, a method includes obtaining a first caliper measurement from a first downhole tool at a depth in a wellbore and obtaining a second caliper measurement from a second downhole tool at the depth in the wellbore. First and second weight factors may be determined. The first weight factors are associated with a reliability of the first caliper measurement under the conditions in which the first caliper measurement was obtained. The second weight factors are associated with a reliability of the second caliper measurement under conditions in which the second caliper measurement was obtained. First and second confidence factors may be determined. The first confidence factor may be determined based at least partly on the first plurality of weight factors, and the second confidence factor may be determined based at least partly on the second plurality of weight factors. Based at least partly on the first caliper measurement, the second caliper measurement, the first confidence factor, and the second confidence factor, an integrated caliper measurement may be determined.

Various refinements of the features noted above may exist in relation to various aspects of this disclosure. Further features may also be incorporated in these various aspects as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to one or more of the illustrated embodiments may be incorporated into any of the above-described aspects of this disclosure alone or in any combination. The brief summary presented above is intended to familiarize the reader with certain aspects and contexts of embodiments of this disclosure without limitation to the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of this disclosure may be better understood upon reading the following detailed description and upon reference to the drawings in which:

FIG. 1 is a partial cross-sectional view of a drilling system that employs a logging-while-drilling (LWD) integrated caliper measurement system, in accordance with an embodiment;

FIG. 2 is a block diagram of the LWD integrated caliper measurement system that provides an integrated caliper based on at least two different types caliper tools, in accordance with an embodiment;

FIG. 3 is a block diagram of the LWD integrated caliper measurement system that provides an integrated caliper based on calipers from an ultrasonic caliper tool and a gamma density tool, in accordance with an embodiment;

FIG. 4 is a diagram comparing the effectiveness of calipers from the ultrasonic caliper tool and the gamma density tool under varying mud conditions, in accordance with an embodiment;

FIG. 5 is a diagram comparing the effectiveness of calipers from the ultrasonic caliper tool and the gamma density tool under varying operating conditions, in accordance with an embodiment;

FIG. 6 is a flowchart of a method for obtaining an integrated caliper measurement representing a weighted average of two or more caliper measurements based on the conditions under which the caliper measurements are made, in accordance with an embodiment;

FIG. 7 is a plot of an example weight factor for a density-derived caliper measurement that represents caliper reliability as a function rotation speed, in accordance with an embodiment;

FIG. 8 is a plot of an example weight factor for an ultrasonic caliper measurement that represents caliper reliability as a function of mud density contrast, in accordance with an embodiment;

FIG. 9 is a block diagram of a system for determining an integrated caliper measurement by weighting at least two different caliper measurements based on varying wellbore conditions, in accordance with an embodiment; and

FIGS. 10-15 are plots illustrating results of case studies using an embodiment of the integrated caliper measurement of this disclosure.

DETAILED DESCRIPTION

One or more specific embodiments of the present disclosure will be described below. These described embodiments are examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, certain features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it may be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.

This disclosure relates to an integrated caliper measurement obtained by combining caliper measurements from two or more downhole tools. Although one caliper measurement from a single tool may not always be accurate under certain conditions, the integrated caliper measurement of this disclosure represents a combined caliper measurement that generally may be better than any one caliper measurement taken individually. Specifically, at least two caliper measurements derived from two different tools or techniques may be obtained. Depending on the conditions under which the caliper measurements were obtained, the individual caliper measurements may be weighted according to the likelihood—under these conditions—that the caliper measurement is reliable. For instance, a number of weight factors may be assigned to each caliper based on the reliability of the caliper measurement under respective conditions. The product of these weight factors may provide total confidence factors associated with the overall reliability of each caliper measurement under those conditions. Based on the confidence factors and the caliper measurements, the integrated caliper measurement may be obtained that outperforms the reliability of either of the composite caliper measurements individually.

Such an integrated caliper measurement system may be used in a logging-while-drilling (LWD) setting. FIG. 1, for example, illustrates a drilling system 10 to drill into a geological formation 12 to produce a wellbore 14. At the surface 16, a drill string 18 that includes a drill bit 20 at its lower end is rotated into the geological formation 12. While the drill string 18 is illustrated in FIG. 1, the embodiments of this disclosure may be used in any suitable downhole device, including work strings and pipe strings. As the drill bit 20 rotates, a “mud” pump 22 forces drilling fluid 24, which may be referred to as “mud” or “drilling mud,” through the drill string 18 to the drill bit 20. The drilling fluid 24, which is used to cool and lubricate the drill bit 20, exits the drill string 18 through the drill bit 20. The drilling fluid 24 may carry drill cuttings 26 out of the wellbore 14 as the drilling fluid 24 flows back to the surface 16. The flow of the drilling fluid 24 out of the wellbore 14 is shown by arrows 28, illustrating that the drilling fluid 24 exits the wellbore 14 through an annulus 30 between the drill string 18 and the geological formation 12. At the surface 16, the drilling fluid 24 is filtered and conveyed back to a mud pit 32 for reuse.

The environment of the wellbore 14 may vary widely depending upon the location and situation of the geological formation 12. For example, rather than a land-based operation, the wellbore 14 may be drilled into the geological formation 12 under water of various depths, in which case the surface 16 may include topside equipment such as an anchored or floating platform, and some of the components used may be positioned at or near a point where the wellbore 14 enters the earth beneath a body of water. Moreover, in the example of FIG. 1, the wellbore 14 is “deviated,” or at least partially horizontal. In other examples, areas of the wellbore 14 that are drilled at any angle other than completely vertical may employ the techniques of this disclosure.

As illustrated in FIG. 1, the lower end of the drill string 18 includes a bottom-hole assembly (“BHA”) 34 that includes the drill bit 20, as well as several drill collars 36, 38 that may include logging-while-drilling (“LWD”) tools 40 and/or measurement-while drilling (“MWD”) tools 42. The LWD tools 40 of FIG. 1 are each housed in a particular area of the drill collar 36, 38, and each may contain any suitable number of logging tools and/or fluid sampling devices. The LWD tools 40 may include capabilities to measure, process, and/or store collected information, as well as to communicate with the MWD tools 42 and/or directly with the surface 16 (e.g., a logging and control computer). A stabilizer 44 may stabilize certain sections of the BHA 34 near the wall 46 of the wellbore 14.

The BHA 34 may include more or fewer LWD tools 40 than those shown in FIG. 1. At least one of the LWD tools 40 may be an LWD integrated caliper tool 40 that can return an integrated caliper measurement based on calipers obtained from two different component tools and/or techniques. Moreover, although this disclosure describes the LWD integrated caliper tool 40 by way of example, downhole tools by other conveyances may obtain the integrated caliper measurements of this disclosure. For example, the LWD integrated caliper tool 40 may alternatively be conveyed as a wireline, slickline, and/or coiled tubing tool.

One example of a logging-while-drilling (LWD) integrated caliper tool 40 appears in FIG. 2. The LWD integrated caliper tool 40 includes at least a first caliper tool 50 and a second caliper tool 52. As will be discussed below, the first caliper tool 50 may be, for example, an ultrasonic caliper tool, and the second caliper tool 52 may be, for example, a radiation-based density-derived caliper tool. In other embodiments, however, the first caliper tool 50 and the second caliper tool 52 may represent any suitable caliber-measuring tools that can return caliper measurements with varying degrees of confidence in varying conditions. In addition, while only the first caliper tool 50 and the second caliper tool 52 appear in FIG. 2, any suitable number of caliper tools may be included in the LWD integrated caliper tool 40. Indeed, other caliper-measuring tools and/or techniques included in the LWD integrated caliper tool 40 may be, for example, a resistivity-derived caliper or a photoelectric-factor-derived caliper. Moreover, since the integrated caliper measurement of this disclosure may be based on any suitable caliper measurements, the LWD integrated caliper tool 40 may include any other suitable caliper measurements now existing or developed in the future.

Data processing circuitry 54 may be located within the LWD integrated caliper tool 40 or elsewhere (e.g., at the surface 16). The data processing circuitry 54 may include a microprocessor (μp) 56, memory (M) 58, and/or storage (S) 60. The data processing circuitry 54 may obtain caliper measurements from the first caliper tool 50 and the second caliper tool 52. Weighting these measurements based on the conditions in the wellbore 14, the data processing circuitry 54 may provide an integrated caliper answer 62. The integrated caliper answer 62 may generally be more accurate over all ranges of depths in the wellbore 14 than the first caliper tool 50 or the second caliper tool 52 alone. The microprocessor 56 may determine the integrated caliper answer 62 based on instructions stored in the memory 58 or the storage 60. The memory 58 and/or the storage 60 thus may represent any suitable article of manufacture that can store these instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, optical storage media, or a hard disk drive, to name a few examples.

The LWD integrated caliper tool 40 may include an ultrasonic caliper tool 70 and a gamma density tool 72, from which to obtain two caliper measurements, in the example of FIG. 3. In one embodiment, the ultrasonic caliper tool 70 and the gamma density tool 72 may generally take the form described by U.S. Pat. No. 7,073,378, “INTEGRATED LOGGING TOOL FOR WELLBORE,” which is assigned to Schlumberger Technology Corporation and incorporated by reference herein in its entirety for all purposes. The ultrasonic caliper tool 70 may include at least one transducer 74 to obtain an ultrasonic caliper measurement. In the example of FIG. 3, the ultrasonic caliper tool 70 includes two transducers 74 disposed 180° from one another. This may allow the ultrasonic caliper tool 70 to obtain a substantially complete caliper measurement even while the LWD integrated caliper tool 40 is not rotating.

The gamma density tool 72 may obtain a caliper measurement derived from a gamma density measurement. The gamma density measurement may be determined from the Compton scattering of gamma-rays that are emitted by a gamma-ray source 76. The gamma-rays emitted by the gamma-ray source 76 may exit the gamma density tool 72 to interact with the materials surrounding the LWD integrated caliper tool 40. Some of the gamma-rays emitted by the gamma-ray source 76 may be detected by a short spaced (SS) detector 78 and others may be detected by a long spaced (LS) detector 80. Based on the number of gamma-rays detected at the SS detector 78 and the LS detector 80, a density measurement may be derived, from which a caliper measurement of the wellbore 14 can be determined. The ultrasonic caliper tool 70 and the gamma density tool 72 may obtain caliper measurements in any suitable fashion, including those well known in the art.

The caliper measurements obtained by the ultrasonic caliper tool 70 and the gamma density tool 72 may respectively prove most reliable under different circumstances. For example, the caliper measurements made by the ultrasonic caliper tool 70 are direct measurements that are azimuthal and may be available in real time. The caliper measurements from the ultrasonic caliper tool 70 may work in drilling fluid 24 of both oil-based mud (OBM) and water-based mud (WBM) and may have a precision of between 0.1 and 0.2 inches in some cases. There are adverse factors, however, that may affect the caliper measurements from the ultrasonic caliper tool 70. These adverse factors include, among other things, the acoustic impedance contrast between the geological formation 12 and the drilling fluid 24, the attenuation of the acoustic signal on which the caliper measurement is based when the drilling fluid 24 is heavy mud, the impact of rugosity of the wellbore 14 on the caliper measurement, and the alignment of the transducers 74 to the wall 46 of the wellbore 14.

For instance, one limiting factor for the caliper measurement from the ultrasonic tool 70 is the mud weight of the drilling fluid 24. Heavy mud attenuates the sonic pulse of the ultrasonic tool 70, reducing the amount of measurable standoff. Also, the strength of the reflected sonic wave output by the ultrasonic tool 70 decreases as the acoustic impedance of the drilling fluid 24 approaches that of the geological formation 12, often preventing precise echo detection, and thus a precise caliper measurement. Other effects that compromise the accuracy of the caliper from the ultrasonic caliper tool 70 include eccentering (e.g., as caused by misalignment between the transducers 74 and the wellbore 14); the impact of cuttings and the rugosity of the wall 46 of the wellbore 14, both of which scatter and reflect the sonic wave of the ultrasonic caliper tool 70; and the effect of gas traveling through the wellbore 14. Moreover, when the ultrasonic caliper tool 70 includes only a single transducer 74, the ultrasonic caliper tool 70 may not get meaningful results when the LWD integrated caliper tool 40 is not rotating. Finally, the accuracy of the ultrasonic caliper tool 70 may depend on the value assumed of the speed of sound through the drilling fluid 24 as used to calculate the caliper measurement from the ultrasonic caliper tool 70. The speed of sound in the drilling fluid 24 may be determined as a function of several environmental parameters, such as mud type, mud density, mud salinity, pressure, temperature, and gas cut. These parameters may be derived from different sources, however, and they may not represent the actual downhole conditions in the wellbore 14. Furthermore, no complete database of sound speed in various drilling fluids 24 is believed to be available, and thus this parameter may be inferred by extrapolation. When the speed of sound is inadvertently wrongly assumed, the caliper measurement from the ultrasonic caliper tool 70 may be inaccurate.

The caliper measurement from the gamma density tool 72 may similarly have strengths and weaknesses. Considering strengths, the caliper derived from the gamma density tool 72 may provide azimuthal measurements and may work when the drilling fluid 24 is oil-based mud (OBM) or water-based mud (WBM). The caliper measurement from the gamma density tool 72 also has good sensitivity to standoff and works in the presence of gas, where the caliper measurement from the ultrasonic tool 70 may sometimes fail. The caliper measurement from the gamma density tool 72 may be limited, however, by certain environmental conditions. For example, a high-barite-weight drilling fluid 24 may cause the caliper measurements from the gamma density tool 72 to be inaccurate. Moreover, the gamma density tool 72 may obtain a good caliper measurement primarily when the stabilizer 44 of the drill string 18 is close in size to the drill bit 20. Furthermore, the theoretical limit of the caliper measurement from the gamma density tool 72 may correspond to the depth of investigation of the LS detector 80. In one example, the results may be reliable up to a maximum of 3 inches under some conditions.

Finally, the caliper measurements from the gamma density tool 72 may be azimuthally available only when the LWD integrated caliper tool 40 is rotating. As such, the caliper measurement from the gamma density tool 72 may not be accurate when the drill string 18 is sliding. As noted above, the term “sliding” refers to the non-rotation of the bottomhole assembly (BHA) 34. This may occur when drilling with a mud motor, tripping into a well, or tripping out of a well, and often happens while traversing valuable depths of the wellbore 14. The accuracy of the caliper from the gamma density tool 72 may also depend on the quality of the measurement used as representative of the density of the geological formation 12, which itself may depend on the accuracy of other downhole tools.

To summarize, calipers from different tools, such as the ultrasonic caliper tool 70 and the gamma density tool 72, each may provide reliable measurements under certain conditions. Some of these conditions may overlap, as generally illustrated in FIGS. 4 and 5. In a plot 90 of FIG. 4, for example, a relationship between the accuracy of caliper measurements from the ultrasonic caliper tool 70 is compared to the accuracy of the caliper measurements from the gamma density tool 72 in varying drilling fluid 24 (“mud”) conditions. Specifically, the accuracy of these separate caliper measurements are compared as obtained in varying amounts of mud photoelectric effect (Pe) values (ordinate 92) and mud weights (abscissa 94) of the drilling fluid 24. As illustrated, an ultrasonic reliability range 96 corresponds to a range of mud conditions in which caliper measurements from the ultrasonic caliper tool 70 are generally reliable and a density caliper range 98 corresponds to a range of mud conditions in which the caliper measurements from the gamma density tool 72 are generally reliable. Outside of the ranges 96 and 98, the respective caliper measurements may become less reliable.

Similarly, a plot 110 of FIG. 5 illustrates ranges of accurate caliper measurements with varying drilling conditions. These include eccentering (ordinate 112) and sliding (abscissa 114). An ultrasonic reliability range 116 corresponds to a range of drilling conditions in which caliper measurements from the ultrasonic caliper tool 70 are generally reliable and a density caliper range 118 corresponds to a range of drilling conditions in which the caliper measurements from the gamma density tool 72 are generally reliable. Outside of the ranges 116 and 118, the respective caliper measurements may become less reliable.

These and other limiting factors that impair the caliper measurements from the ultrasonic caliper tool 70 and the caliper from the gamma density tool 72 are generally shown in the following table:

TABLE 1 Limiting factor Ultrasonic Density Mud/Formation X X Contrast DOI X X Mud Pe X Mud Weight X X Mud Salinity Rugosity X Eccentering X Sliding XXX

In Table 1 above, several limiting factors are listed that respectively may affect the accuracy of calipers from the ultrasonic caliper tool 70 or from the gamma density tool 72. An “X” indicates that the listed limiting factor affects caliper measurements from the ultrasonic caliper tool 70 or the gamma density tool 72. As mentioned above, these limiting factors include the contrast between the drilling fluid 24 and the geological formation 12 (mud/formation contrast), the depth of investigation (DOI) of the respective tools 70 and 72, the photoelectric (Pe) factor associated with the drilling fluid 24, the weight of the drilling fluid 24 (mud weight), the salinity of the drilling fluid 24 (mud salinity), the rugosity of the wellbore 14, the amount of eccentering of the LWD integrated caliper tool 40, and/or whether or not the BHA 34 is sliding.

As indicated by FIGS. 4 and 5 and by Table 1, the caliper measurement from the ultrasonic caliper tool 70 is the measurement of choice in drilling scenarios characterized by high values of Pe of the drilling fluid 24. The caliper derived from the gamma density tool 72, on the other hand, may be preferred in cases of high mud weight of the drilling fluid 24. For the case of small tool eccentering, the caliper measurement from the gamma density tool 72 may perform more reliably than the ultrasonic caliper tool 70 if the LWD integrated caliper tool 40 is run eccentered. In cases involving significant amounts of sliding, however, the ultrasonic caliper tool 70 may provide a reliable measurement (provided the ultrasonic caliper tool 70 includes two transducers 74 oppositely disposed), while the caliper measurement from the gamma density tool 72 may be substantially completely unreliable under such circumstances.

All of the above-described scenarios are, of course, simplified to some degree. Reality is more complex, and several other factors may be considered. The full spectrum of measurements acquired by the tools of the BHA 34 and the knowledge of the environmental parameters may permit estimation of the quality of the caliper measurements from each respective tool in many different circumstances. Because different caliper measurements from different caliper tools may be more or less appropriate under different circumstances, the LWD integrated caliper tool 40 may combine the caliper measurements derived from these various techniques (e.g., from the ultrasonic caliper tool 70 and the gamma density tool 72) that may, in combination, have an enhanced accuracy and wider applicability range compared to the caliper measurements taken individually.

Indeed, as seen by a flowchart 130 of FIG. 6, the LWD integrated caliper tool 40 may obtain a first caliper measurement from a first caliper tool (e.g., the ultrasonic caliper tool 70) (block 132) and obtain a second caliper measurement from a second caliper tool (e.g., the gamma density tool 72) (block 134). As will be described further below, the data processing circuitry 54 may determine a confidence factor for each of the caliper measurements according to various weight factors associated with the conditions under which the caliper measurements where obtained (block 136). The data processing circuitry 54 may transform the various single caliper measurements into the combined integrated caliper answer 62 by ascertaining a weighted average of the caliper measurements according to the respective confidence factors (block 138).

In this way, the integrated caliper answer 62 may be thought of as generally the best available caliper from those collected by the LWD integrated caliper tool 40 at a particular depth, depending on the conditions under which the caliper measurements are obtained. The contribution of each caliper measurement in the ultimate integrated caliper answer 62 may depend on the confidence factor associated with each caliper measurement as determined at block 136. As will be discussed below, there may be one confidence factor per caliper measurement, each confidence factor being determined based on one or a group of weight factors.

The weight factors used to ascertain the confidence factors may be values between 0 and 1 that qualify the conditions in which the LWD integrated caliper tool 40 is working. These values may be obtained from characteristics curves that represent the effect of a particular parameter on the particular caliper measurement (e.g., the effect of tool sliding on the reliability of the caliper from the gamma density tool 72). In one example, these curves or functions may take the following form:

${{{Weight}\mspace{14mu} {Factor}} = \frac{1}{1 + ^{\frac{({x - a})}{b}}}},$

where the terms a and b are constants that control the slope of the curve of the weight factor, and x is the parameter to evaluate.

Every weight factor may have a particular function shape associated with it. Namely, each weight factor may be computed as a function of a particular parameter or measurement that defines the function shape. The functions may be derived from experimental databases, measurement specifications, field data, and/or computer modeling. Some examples of functional forms of weight factors appear in FIGS. 7 and 8. In FIG. 7, a plot 150 provides a weight factor WDRPM (ordinate 152) as a function of the rotation speed of the LWD integrated caliper tool 40 (abscissa 154). The weight factor WDRPM is a value between 0 and 1 representing the reliability of the caliper measurement from the gamma density tool 72 as the rotation speed of the LWD integrated caliper tool 40 changes. A curve 156 shows the accuracy of the gamma density tool 72 improving as the rotation speed of the LWD integrated tool 40 increases. In the particular example of FIG. 7, the gamma density tool 72 may be substantially unreliable under 10 RPM, but may be substantially reliable at 30 RPM or higher. The reliability may increase dramatically between 10 RPM and 30 RPM.

In FIG. 8, a plot 160 illustrates a weight factor WUABS (ordinate 162) as a function of the density contrast of the drilling fluid 24 (abscissa 164). The weight factor WUABS is shown to be a value between 0 and 1 representing the reliability of the caliper measurement from the ultrasonic caliper tool 70 as the density contrast of the drilling fluid 24 increases. In the example of FIG. 8, a weighting curve 166 illustrates how the ultrasonic caliper tool 70 may become increasingly more accurate as the density contrast of the drilling fluid 24 improves. That is, all things being equal, a density contrast of the drilling fluid 24 in relation to the geological formation 12 near 0 will produce an inaccurate caliper measurement from the ultrasonic caliper tool 70, while a density contrast of the drilling fluid 24 and the geological formation 12 above around 1.2 may produce an accurate caliper measurement from the ultrasonic caliper tool 70. It should be appreciated that the weighting functions illustrated in FIGS. 7 and 8 are provided by way of example, and actual implementations may vary depending on the particular experimental database information, measurement specifications, field data, and/or computer modeling associated with the particular tools used to obtain the caliper measurements.

An example of how the weight factors may be used to obtain the integrated caliper answer 62 appears in a system 170 of FIG. 9. As seen in FIG. 9, first inputs 172 to the system 170 may relate to the caliper measurement from the ultrasonic caliper tool 70 and second inputs 174 may relate to the caliper measurement from the gamma density tool 72. From the first inputs 172, first weight factors 176 may be determined that relate to the reliability of the caliper measurement from the ultrasonic caliper tool 70 under the conditions indicated by the first inputs 172. From the second inputs 174, second weight factors 178 may be determined that relate to the caliper measurement from the gamma density tool 72 under the conditions indicated by the second inputs 174.

In the particular example shown in FIG. 9, the first inputs 172 may include an indication of the standoffs used to obtain the caliper from the ultrasonic caliper tool 70, an average ultrasonic caliper value obtained from the ultrasonic caliper tool 70, a collar rotation speed (CRPM), at rate of penetration (ROP) of the drill string 18 into the wellbore 14, a size of the stabilizer 44 of the drill string 18, a mud weight of the drilling fluid 24, a mud type of the drilling fluid 24 (e.g., oil-based mud (OBM) or water-based mud (WBM)), a size of the drill bit 20, and/or a slowness of the drilling fluid 24. The first inputs 172 may also include an average ultrasonic caliper measurement (UCAV) value. The first inputs 172 may be used to determine the first weight factors 176. Examples of the various weight factors 176 that may be determined appear below with reference to Table 2.

The second inputs 174 may include the standoffs of the gamma density tool 72, the collar rotation speed (CRPM), the rate of penetration of the drill string 18 into the wellbore 14 (ROP), a size of a stabilizer of the drill string 18, a size of the stabilizer 44 of the drill string 18, a mud weight of the drilling fluid 24, a mud type of the drilling fluid 24 (e.g., oil-based mud (OBM) or water-based mud (WBM)), a size of the drill bit 20, and/or a slowness of the drilling fluid 24. In addition, the second inputs 174 may include a bottom bulk density (ROBB), a bottom bulk density correction (DRHB), and a volumetric photoelectric factor value (U), which may be obtained by the gamma density tool 72 or any other suitable downhole tool. These additional inputs may be used to correct the caliper measurement from the gamma density tool 72 in addition to determining the second weighting values 178. The second inputs 174 may also include an average caliper measurement value from the gamma density tool 72 (DCAV). The second inputs 174 may be used to determine the second weight factors 178.

The weight factors 176 and 178 relate the reliability of the ultrasonic caliper tool 70 and gamma density tool 72, respectively, depending on the conditions indicated by the first inputs 172 and the second inputs 174, respectively. Examples of some weight factors 176 and 178 are provided below in Table 2:

TABLE 2 OUTPUTS DEN Weight Factor WDU Density Weight U DEN Weight Factor WDMD Density Weight Mud Weight DEN Weight Factor WDECC Density Weight Eccentricity DEN Weight Factor WDABS Density Weight Absolute Values DEN Weight Factor WDRQF Density Weight Density Quality DEN Weight Factor WDRPM Density Weight CRPM DEN Weight Factor WDROP Density Weight ROP US Weight Factor WUIMP Ultrasonic Weight Impedance US Weight Factor WUMD Ultrasonic Weight Mud Weight US Weight Factor WUECC Ultrasonic Weight Eccentricity US Weight Factor WUABS Ultrasonic Weight Absolute Values US Weight Factor WURQF Ultrasonic Weight Ultrasonic Quality US Weight Factor WURPM Ultrasonic Weight CRPM US Weight Factor WUROP Ultrasonic Weight ROP

In Table 2 above, the first weight factors 176 are ultrasonic caliper weight factors denoted by “US” and the second weight factors 178 are density-derived caliper weight factors denoted by “DEN.” In one embodiment, the weight factors 176 and 178 illustrated in FIG. 2 each may represent a value between 0 and 1 as determined by a function of the reliability of the caliper measurement under a particular condition. The functions underlying the weight factors 176 and 178 may be determined based on experimental database information, measurement specifications, field data, and/or computer modeling in relation to each caliper tool.

Separate confidence factors relating to each caliper measurement may be ascertained as the product of all of the individual weight factors 176 or 178 relating to that caliper measurement. In the example of FIG. 9, the product of the second weight factors 176, which relate to the ultrasonic caliper tool 70, may produce a confidence factor for ultrasonic caliper (UCQF). The product of the second weight factors 178, which relate to the gamma density tool 72, may produce a confidence factor for density caliper (DCQF). A weighted average of the confidence factor for ultrasonic caliper (UCQF) and the confidence factor for density caliper (DCQF) may be used to determine a confidence factor for the integrated caliper answer 162 as a weighted average of these confidence factors as follows:

I C Q F = ndcqf ⋅ D C Q F + nucqf ⋅ U C Q F, where: ${{ndcqf} = \frac{D\; C\; Q\; F}{{D\; C\; Q\; F} + {U\; C\; Q\; F}}};{and}$ ${nucqf} = {\frac{U\; C\; Q\; F}{{D\; C\; Q\; F} + {U\; C\; Q\; F}}.}$

The values nucqf and ndcqf may be referred to as normalized confidence factors associated with the ultrasonic caliper tool 70 and the gamma density tool 72, respectively. The sum of the normalized confidence factors nucqf and ndcqf is 1. In other words, the higher the confidence factor associated with a caliper from a particular tool (e.g., the ultrasonic caliper tool 70 or the gamma density tool 72), the greater the contribution of that caliper measurement to the final value of the integrated caliper answer 62. The integrated caliper answer 62 appears in FIG. 9 as ICAL, and may be defined as a weighted average of the individual caliper measurements from the ultrasonic caliper tool 70 (UCAB) and the gamma density tool 72 (DCAB) as follows:

ICAL=ndcqf·DCAV+nucqf·UCAV.

The resulting integrated caliper answer 62 (ICAL) may represent the most appropriate measurement from among the various caliper measurements available through the data set being analyzed. The value of the integrated caliper answer 62 from the LWD integrated caliper tool 40 has been born out through several case studies, which will be described below. In a first case study, a data set including caliper measurements from an ultrasonic caliper tool 70 and caliper measurements from a gamma density tool 72 were considered in a logging-while-drilling setting with the following conditions:

TABLE 3 Depth Interval (ft) 7470-8476 Mud Type OBM Deviation (deg)  0-88 Mw (lb/gal) 10.3 Hole Size (in.) 8½ Mud DT (μs/ft) 211 Stab size (in.) 7⅞ Salinity (ppk) 20 Lithology Carbonate/ shale

FIGS. 10-13 represent plots of caliper measurements and confidences under the case study conditions indicated above and using the integrated caliper technique of this disclosure. In this first case study, the caliper data was subject to quality-control processes before the analysis of these data to obtain the integrated caliper answer 62 (ICAL). A plot 180 of FIG. 10 describes a relationship between the wellbore 14 caliper measurement in inches (ordinate 182) over a depth interval from about 7470 to 7700 feet (abscissa 184). A curve 186 represents the average density caliper measurement (DCAV), a curve 188 represents the average ultrasonic caliper measurement (UCAV), and a curve 190 represents the integrated caliper answer 62 (ICAL). A plot 191 of FIG. 11 describes a relationship between confidence factors of the caliper measurements (QF) from 0 to 1 (ordinate 192) over the same depth interval (abscissa 194). In the plot 191, a curve 195 represents the confidence factor of the density caliper (DCQF), a curve 196 represents the confidence factor of the ultrasonic caliper (UCQF), and a curve 197 represents the confidence factor of the integrated caliper (ICQF).

In the earlier areas of the depth interval shown in the plot 180 of FIG. 10, the curve 186 representing the average density caliper measurement (DCAV) is wildly different from the caliper measurement from the ultrasonic caliper tool 70 (UCAV) of curve 188 and the integrated caliper answer 62 (ICAL) of the curve 190. Indeed, the curve 186 would appear to indicate a huge washout, while the integrated caliper answer 62 (ICAL) of curve 190 and the ultrasonic caliper measurement (UCAV) of curve 188 indicates a good condition of the wellbore 14. In this case study, the reality is that in this depth interval, the LWD integrated caliper tool 40 is still within the well casing 22. Here, it is noted that the integrated caliper answer 62 (ICAL) 190 appears to provide a proper caliper measurement throughout the depth interval of the plot 180 despite radical differences between the caliper measurement from the gamma density tool 72 (DCAV) of the curve 186 and the caliper measurement from the ultrasonic caliper tool 70 (UCAV) of the curve 188.

The accuracy of the respective caliper measurements is reflected in the confidence factors plotted in plot 191. In the depths where the average density caliper (DCAV) of curve 186 appears (inaccurately) to indicate a washout, the density caliper confidence factor (DCQF) of curve 195 is at 0. Even so, the ultrasonic caliper confidence factor (UCQF) of curve 196 and integrated caliper confidence factor (ICQF) of curve 197 remain high.

FIGS. 12 and 13 relate to a depth interval of the first case study between 7900 and 8200 feet. These depths include moments of areas of sliding (e.g., between 7915-7925 feet, 7950-7995 feet, 8010-8025 feet, 8045-8055 feet, and 8075-8090 feet). Specifically, FIG. 12 represents a plot 200 of the caliper measurements of the wellbore in inches (ordinate 202) over a depth interval (ordinate 204). A curve 206 represents a caliper measurement from the gamma density tool 72 (DCAV), a curve 208 represents a caliper measurement from the ultrasonic caliper tool 70 (UCAV), and a curve 210 represents the integrated caliper answer 62 (ICAL). A plot 220 of FIG. 13 provides corresponding confidence factors associated with the caliper measurements plotted in FIG. 12. In the plot 220, various confidence factor values from 0-1 (ordinate 222) are compared to the same depth interval (abscissa 224). A curve 226 represents a confidence factor associated with the gamma density tool 72 (DCQF), a curve 228 represents a confidence factor for the ultrasonic caliper tool 70 (UCQF), and a plot 230 represents the confidence factor of the integrated caliper answer 62 (ICQF).

As can be seen in FIGS. 12 and 13, throughout the depths in which sliding takes place, the caliper measurement from the gamma density tool 72 becomes ineffective. This is illustrated by the loss of the confidence factor DCQF to a value of 0 for the curve 226 and the corresponding erratic behavior of the curve 206 at these depths. Even so, the integrated caliper answer 62 (ICAL) of the curve 210 remains quite accurate—the integrated confidence factor ICQF of the curve 230 approaches 95% during depths where sliding is not taking place. When sliding is taking place, the integrated confidence factor ICQF of the curve 230 remains equal to that of the ultrasonic confidence factor (UCQF) of curve 228. The lower confidence factor of the ultrasonic caliper measurement to about 0.5 may be a result of the weight factor WURPM, which may be around 0.5 owing to a low collar rotational velocity (CRPM). This weight factor may be reduced to 0.5 because ultrasonic caliper tool 70 is not rotating and, while still providing a useful result, may not be as reliable as when rotating.

A second case study also illustrates the effectiveness of the integrated caliper technique of this disclosure. The second case study involves conditions as provided by Table 4 below:

TABLE 4 Depth Interval (ft) 6815-9027 Mud Type WBM Deviation (deg) 0.5-1.2 Mw (lb/gal) 8.53 Hole Size (in.) 8½ Mud DT (μs/ft) 180 Stab size (in.) 8¼ Salinity (ppk) 38 Lithology Sandy/Shaly sand

An example of results obtained in this second case study appear in FIGS. 14 and 15. FIG. 14 represents a plot 240 of illustrating caliper measurements of the wellbore 14 in inches (ordinate 242) over a depth interval (abscissa 244). A curve 246 illustrates a density caliper measurement (DCAV), a curve 248 represents an ultrasonic caliper measurement (UCAV), and a curve 250 represents the integrated caliper answer 62 (ICAL). A plot 260 of FIG. 15 corresponds to the same depth interval of plot 240 of FIG. 14. The plot 260 represents a confidence factor from 0-1 (ordinate 262) over the depth interval (abscissa 264). A curve 266 represents the confidence interval associated with the gamma density tool 72 (DCQF), a curve 268 represents a confidence interval associated with the ultrasonic caliper tool 70 (UCQF), and a plot 270 represents the integrated caliper answer 62 (ICQF).

As seen in FIGS. 14 and 15, the agreement on both the ultrasonic and density caliper measurements is remarkable for the depth interval 7630-7980 feet. Indeed, in FIG. 14, the integrated caliper answer 62 (ICAL) of curve 250 overlays well with both the density caliper measurement curve 246 and the ultrasonic caliper curve 248, and the confidence of all three of these is high, as seen by plots 266, 268, and 270 of the plot 260 of FIG. 15. Indeed, the separation is on the order of tenths of an inch, showing even the rugosity of the wellbore 14. The scale shown in the plot 240 of FIG. 14 has been amplified to note the similarity of the answers from the ultrasonic caliper tool 70 and the gamma density tool 72. Over the interval 8000-8160 feet, the confidence of the density caliper measurement (DCQF) of curve 266 of FIG. 15 drops dramatically and, as a result, the integrated caliper answer 62 (ICAL) of the curve 250 of FIG. 14 separates from the density caliper measurement (DCAV) of the curve 246. In this example, it is believed that the decrease in the confidence of the gamma density tool 72 in this interval is driven primarily by weight factors WDRQF which relates to the ROBB value, and WDU, which relates to the photoelectric factor of the drilling fluid 24.

Although the integrated caliper measurement of this disclosure has been described in a logging-while-drilling (LWD) implementation, the integrated caliper system of this disclosure may be used with any suitable means of conveyance and should not be understood to be limited as such. Moreover, while the integrated caliper measurement of this disclosure may benefit from component caliper measurements obtained by different tools in the same sub and/or logging run, caliper data from different tools and/or logging runs may be used in a post-hoc determination of the integrated caliper measurement at a later time (provided the caliper measurements by multiple tools can be aligned by depth and the particular environmental conditions associated with each caliper measurement can be ascertained or estimated).

The specific embodiments described above have been shown by way of example, and it should be understood that these embodiments may be susceptible to various modifications and alternative forms. Finally, it should be further understood that the claims are not intended to be limited to the particular forms disclosed, but rather to cover modifications, equivalents, and alternatives falling within the spirit and scope of this disclosure. 

What is claimed is:
 1. A system comprising: a plurality of caliper tools configured to obtain respective caliper measurements of a wellbore; and data processing circuitry configured to assign respective confidence factors to weight the respective caliper measurements and combine the weighted caliper measurements to obtain an integrated caliper measurement, wherein the confidence factors are determined based at least partly on at least two of a plurality of weighting functions that each relate a confidence of the caliper measurements to an environmental or drilling characteristic occurring when the caliber measurements are obtained.
 2. The system of claim 1, wherein the plurality of caliper tools comprises an ultrasonic caliper tool configured to obtain an ultrasonic caliper.
 3. The system of claim 1, wherein the plurality of caliper tools comprises a gamma density tool configured to obtain a density-derived caliper.
 4. The system of claim 1, wherein the plurality of caliper tools comprises three or more caliper tools that provide three or more respective caliper measurements.
 5. The system of claim 1, wherein the data processing circuitry is configured to assign the respective confidence factors to the respective caliper measurements based at least in part on a characteristic of drilling fluid in the wellbore.
 6. The system of claim 5, wherein the characteristic of the drilling fluid in the wellbore comprises a mud weight of the drilling fluid, a mud type of the drilling fluid, a mud slowness of the drilling fluid, or a photoelectric factor associated with the drilling fluid, or any combination thereof.
 7. The system of claim 1, wherein the data processing circuitry is configured to assign the respective confidence factors to the respective caliper measurements based at least in part on a characteristic of operation of a drill string that houses the plurality of caliper tools.
 8. The system of claim 7, wherein the characteristic of operation of the drill string comprises a rotation speed of the drill string, an amount of eccentering of the drill string in the wellbore, or a rate of penetration of the drill string in the wellbore, or any combination thereof.
 9. The system of claim 1, wherein the data processing circuitry is configured to assign the respective confidence factors to the respective caliper measurements based at least in part on a condition of the wellbore or of a drill string that houses the plurality of caliper tools, wherein the condition is configured to be input by a human operator of the system.
 10. The system of claim 1, comprising at least one other tool configured to ascertain a condition of the wellbore or of a drill string that houses the plurality of caliper tools, wherein the data processing circuitry is configured to assign the respective weights to the respective caliper measurements based at least in part on the condition of the wellbore.
 11. One or more tangible non-transitory machine-readable media storing instructions to: receive a first caliper measurement deriving from a first downhole tool; receive a second caliper measurement deriving from a second downhole tool; receive a plurality of conditions under which the first downhole tool obtained the first caliper measurement and under which the second downhole tool obtained the second caliper measurement; determine a first confidence factor representing a degree of confidence that the first caliper measurement is accurate based at least in part on a plurality of weighting factors each associated with one of the plurality of conditions; determine a second confidence factor representing a degree of confidence that the second caliper measurement is accurate based at least in part on a plurality of weighting factors each associated with one of the plurality of conditions; and determine an integrated caliper measurement using the first caliper measurement, the first confidence factor, the second caliper measurement, and the second confidence factor.
 12. The machine-readable media of claim 11, wherein: the instructions to determine the first confidence factor comprise instructions to determine a first plurality of weight factors each relating to a response of the first downhole tool to at least two of the plurality of conditions and determine the first confidence factor based at least in part on the first plurality of weight factors; and the instructions to determine the second confidence factor comprise instructions to determine a second plurality of weight factors each relating to a response of the second downhole tool to at least two of the plurality of conditions and determine the second confidence factor based at least in part on the second plurality of weight factors.
 13. The machine-readable media of claim 12, wherein: the instructions to determine the first confidence factor comprise instructions to multiply the first plurality of weight factors together, wherein each of the first plurality of weight factors represents a value between 0 and 1; and the instructions to determine the second confidence factor comprise instructions to multiply the second plurality of weight factors together, wherein each of the second plurality of weight factors represents a value between 0 and
 1. 14. The machine-readable media of claim 11, wherein the instructions to determine the integrated caliper measurement comprise instructions to weight the first caliper measurement based on a relationship between the first confidence factor to the second confidence factor and to weight the second caliper measurement based on a relationship between the second confidence factor to the first confidence factor.
 15. The machine-readable media of claim 11, wherein the instructions to determine the integrated caliper measurement accord with the following relationships: I C A L = ndcqf ⋅ D C A V + nucqf ⋅ U C A V; ${{ndcqf} = \frac{D\; C\; Q\; F}{{D\; C\; Q\; F} + {U\; C\; Q\; F}}};{and}$ ${{{nucqf} = \frac{U\; C\; Q\; F}{{D\; C\; Q\; F} + {U\; C\; Q\; F}}};}$ where ICAL represents the integrated caliper measurement, DCAV represents the first caliper measurement, UCAV represents the second caliper measurement, DCQF represents the first confidence factor, and UCQF represents the second confidence factor.
 16. The machine-readable media of claim 11, comprising instructions to determine a confidence factor of the integrated caliper measurement in accordance with the following relationships: I C Q F = ndcqf ⋅ D C Q F + nucqf ⋅ U C Q F; ${{ndcqf} = \frac{D\; C\; Q\; F}{{D\; C\; Q\; F} + {U\; C\; Q\; F}}};{and}$ ${{nucqf} = \frac{U\; C\; Q\; F}{{D\; C\; Q\; F} + {U\; C\; Q\; F}}};$ where ICQF represents the confidence factor of the integrated caliper measurement, DCQF represents the first confidence factor, and UCQF represents the second confidence factor. 